Solving the Square Well With a Bump and Python. Bumpy With Numpy and the Eigenvalue Problem.
An infinite square well has a bump potential on one side. We can solve this by using the finite difference method to create the equation as a matrix and then use the eigenvalue problem to find the energies and eigenvectors.
Yes, you need to use python with numpy.
00:00 - Intro
02:13 - Finite Difference
05:04 - Schrödinger equation as a finite difference
08:19 - Building a matrix
11:06 - Moving to python
12:46 - setting up constants
17:23 - Building the Hamiltonian
23:19 - Solving the Eigenvalue problem
27:51 - Normalization